Synchronization of two self-excited pendula: Influence of coupling structure's parameters

In this paper we investigate the possibilities and scenarios of synchronization under the influence of parameters of structure that couples oscillators. The research is based on a simple model of two pendula with van der Pol damping type, suspended on a horizontally oscillating beam. The regions of existence and co-existence of different synchronization patterns are shown, and typical bifurcation scenarios between types of model's responses are presented. The behavior of each pendulum is analyzed, and the reasons of bifurcations are explained using the energy balance method. Moreover, we investigate the basins of attraction of considered system, exhibiting their complicated structure along with statistical study on attractors' occurrence. Our results are presented for simple one parameter variation, as well as for group of parameters varied, when the influence of coupling structure's parameters on appearance of observed patterns is studied. Our results refer to a simple and typical mechanical model of coupled oscillators, emphasizing their universality in dynamical systems of engineering type.